Bipolar neutrosophic sets and their application based on multi-criteria decision making problems
Bipolar neutrosophic sets and their application based on multi-criteria decision making problems
In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted average operator and bipolar neutrosophic weighted geometric operat��r to aggregate the bipolar neutrosophic information. Furthermore, based on the neutrosophic weighted geometric(aritmetic) operat��r and the score, certainty and accuracy functions, we develop a bipolar neutrosophic multiple criteria decision-making approach, in which the evaluation values of alternatives on the attributes take the form of bipolar neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method.
Thanks
- University of New Mexico United States
- Department of Mathematics
- Kilis 7 Aralık University Turkey
- Kilis 7 Aralık University Turkey
- Quaid-i-Azam University Pakistan
Composite material, Artificial intelligence, bipolar neutrosophic set, Social Sciences, Group Decision Making, Set (abstract data type), Multi-Criteria Decision Making, Management Science and Operations Research, Operator (biology), Biochemistry, Gene, Neutrosophic set, Decision Sciences, Multi-Objective Transportation Problem Optimization, bipolar neutrosophic sets, Engineering, Neutrosophic set, General Mathematics (math.GM), FOS: Mathematics, Multi-criteria Decision Making, Mathematics - General Mathematics, Data mining, GIS-based Decision Analysis, Application of Soft Set Theory in Decision Making, geometric operator, Computer science, Materials science, Programming language, Algorithm, Chemistry, Aggregate (composite), Control and Systems Engineering, Physical Sciences, Repressor, Transcription factor, Mathematics, Decision-making
Composite material, Artificial intelligence, bipolar neutrosophic set, Social Sciences, Group Decision Making, Set (abstract data type), Multi-Criteria Decision Making, Management Science and Operations Research, Operator (biology), Biochemistry, Gene, Neutrosophic set, Decision Sciences, Multi-Objective Transportation Problem Optimization, bipolar neutrosophic sets, Engineering, Neutrosophic set, General Mathematics (math.GM), FOS: Mathematics, Multi-criteria Decision Making, Mathematics - General Mathematics, Data mining, GIS-based Decision Analysis, Application of Soft Set Theory in Decision Making, geometric operator, Computer science, Materials science, Programming language, Algorithm, Chemistry, Aggregate (composite), Control and Systems Engineering, Physical Sciences, Repressor, Transcription factor, Mathematics, Decision-making